THIS INVENTION relates particularly to a method of reconstructing tomographic images which can be used, for example, in radiological applications.
The tomographic reconstruction of an object""s density distribution from its projections which are images of the object taken from different directions, is of particular interest in the medical field and other fields including electron microscopy, astronomy, geology and non-destructive testing.
In many instances it is impossible to acquire usable projection measurements over a full 360xc2x0 angular range. Furthermore, in medical applications, the exposure of patients to X-ray radiation should be minimised. It is also time-consuming, expensive and may require a large amount of resources to acquire a complete data set. In the case of electron microscopy, the density distribution may be such that X-rays will be attenuated in certain angular ranges, thereby resulting in a poor signal to noise ratio for those projections.
The abovementioned problems encourage the use of tomographic image reconstruction techniques which make use of incomplete projection data, such as limited angle tomography.
In limited angle tomography, the angular range of available projections is restricted. The required number of projections and the minimum angular range for performing a reconstruction will depend on the complexity of the image to be reconstructed. A number of problems have been identified with existing limited angle tomography reconstruction techniques. Existing techniques make use of iterative methods wherein prior knowledge is applied in the same way to each pixel (image element) without regard to its location in the image. The prior knowledge is typically in the form of space invariant information such as prior knowledge of the possible density levels or piece-wise smoothness that regions of the object can assume.
The problem with this approach wherein the prior knowledge is applied to each pixel in the same way, is that it forces certain pixels to assume values that are incorrect in the final reconstruction. This leads to poor quality reconstructions having an unacceptably high visibility of distortions particularly in the case of severely limited angular ranges of measured projections. Existing techniques also do not teach how to recover unmeasured edge information when the angular range of measured projections is increasingly reduced.
It is an object of the present invention to ameliorate many of the problems associated with existing limited angle tomographic reconstruction techniques.
Any reference hereinafter to xe2x80x9climited angle tomographyxe2x80x9d must be interpreted to mean the reconstruction of tomographic images wherein the angular range of available projections is restricted.
Any reference hereinafter to xe2x80x9cprior knowledgexe2x80x9d must be interpreted to mean space invariant information on at least one of a group consisting of possible density levels and piece-wise smoothness that regions of an object for which a tomographic image is to be reconstructed, can assume.
According to a first aspect of the invention there is provided a method of reconstructing a tomographic image of an object from incomplete projection data using a limited angle tomography technique, the method including the steps of:
using the projection data to obtain a first reconstruction of the image;
creating an intermediate image in which each pixel represents the probability that a corresponding pixel of the first reconstruction of the image resembles the corresponding pixel of a final reconstruction of the image;
based on the intermediate image, identifying regions in the first reconstruction of the image that resemble their final reconstruction;
applying prior knowledge only to said regions in the first reconstruction of the image that resemble their final reconstruction, to obtain a second reconstruction of the image which is more accurate than the first reconstruction;
applying the projection data to projections of the second reconstruction of the image by constraining the projections of the second reconstruction of the image to the projection data, to obtain a third reconstruction of the image which is more accurate than the second reconstruction; and
iteratively creating intermediate images, identifying regions in the third reconstruction of the image and subsequent reconstructions of the image, that resemble their final reconstruction and applying the prior knowledge and the projection data in the same way to the third reconstruction of the image and subsequent reconstructions thereof until a final reconstruction is achieved.
The method may include iteratively applying the projection data to projections of reconstructions of the image by constraining the projections to the projection data using an iterative update equation method wherein the resultant error obtained between calculated projections of each reconstruction and the projection data is repeatedly back-projected onto the reconstructions so that the error decreases in subsequent reconstructions of the image.
The method may include applying the prior knowledge to reconstructions of the image by thresholding preselected pixels to the closest intensity value.
According to a second aspect of the invention there is provided a computer program product for reconstructing a tomographic image of an object from incomplete projection data using a limited angle tomography technique, the computer program product including program instructions for:
using the projection data to obtain a first reconstruction of the image;
creating an intermediate image in which each pixel represents the probability that a corresponding pixel of the first reconstruction of the image resembles the corresponding pixel of a final reconstruction of the image;
based on the intermediate image, identifying regions in the first reconstruction of the image that resemble their final reconstruction;
applying prior knowledge only to said regions in the first reconstruction of the image that resemble their final reconstruction, to obtain a second reconstruction of the image which is more accurate than the first reconstruction;
applying the projection data to projections of the second reconstruction of the image by constraining the projections of the second reconstruction of the image to the projection data, to obtain a third reconstruction of the image which is more accurate than the second reconstruction; and
iteratively creating intermediate images, identifying regions in the third reconstruction of the image and subsequent reconstructions of the image, that resemble their final reconstruction and applying the prior knowledge and the projection data in the same way to the third reconstruction of the image and subsequent reconstructions thereof until a final reconstruction is achieved.
The computer program product may include program instructions for iteratively applying the projection data to projections of reconstructions of the image by constraining the projections to the projection data using an iterative update equation method wherein the resultant error obtained between calculated projections of each reconstruction and the projection data is repeatedly back-projected onto the reconstructions so that the error decreases in subsequent reconstructions of the image.
The computer program product may include program instructions for applying the prior knowledge to reconstructions of the image by thresholding preselected pixels to the closest intensity value.
According to a third aspect of the invention there is provided processing means having software executable thereon for reconstructing a tomographic image of an object from incomplete projection data using a limited angle tomography technique, the software being configured to:
use the projection data to obtain a first reconstruction of the image;
create an intermediate image in which each pixel represents the probability that a corresponding pixel of the first reconstruction of the image resembles the corresponding pixel of a final reconstruction of the image;
based on the intermediate image, identify regions in the first reconstruction of the image that resemble their final reconstruction;
apply prior knowledge only to said regions in the first reconstruction of the image that resemble their final reconstruction, to obtain a second reconstruction of the image which is more accurate than the first reconstruction;
apply the projection data to projections of the second reconstruction of the image by constraining the projections of the second reconstruction of the image to the projection data, to obtain a third reconstruction of the image which is more accurate than the second reconstruction; and
iteratively create intermediate images, identify regions in the third reconstruction of the image and subsequent reconstructions of the image, that resemble their final reconstruction and apply the prior knowledge and the projection data in the same way to the third reconstruction of the image and subsequent reconstructions thereof until a final reconstruction is achieved.
The software executable thereon may be configured to iteratively apply the projection data to projections of reconstructions of the image by constraining the projections to the projection data using an iterative update equation method reconstruction and the projection data is repeatedly back-projected onto the reconstructions so that the error decreases in subsequent reconstructions of the image.
The software may be configured to apply the prior knowledge to reconstructions of the image by thresholding preselected pixels to the closest intensity value.